I'm also a first time mum, used to get average 20ml each session in the first month, then 30-40ml in the 5-6th weeks and almost gave up. I didn't engage those masseur to check for blockage but my supply has increased over time, so it's unlikely I had any blockage.
Baby is 2.5 months old now, my supply now fluctuates between 80ml to 110ml -- still not a lot but at least there's improvement.
I latch all the time except after midnight till early morning. I wake up in the middle of the night every 3 hours to pump.